LEADER 01436nam 2200361 n 450 001 996390025803316 005 20221108070203.0 035 $a(CKB)4940000000101226 035 $a(EEBO)2240871424 035 $a(UnM)99837406 035 $a(EXLCZ)994940000000101226 100 $a19901004d1589 uy | 101 0 $aeng 135 $aurbn||||a|bb| 200 02$aA godlie and short discourse$b[electronic resource] $eshewing not onely what time the inhabitants of this land first receyued the Christian faith: but also what maner of doctrine was planted in the same. Whereby may appeare, howe the reformation at this day in England is not a bringing in of a newe religion, but a reducing againe of the olde and auncient fayth 210 $aLondon $cPrinted by Iohn Wolfe$d1589 215 $a[4], 44 leaves 300 $aBy Christopher Rosdell. 300 $aRunning title reads: The ancient faith of England. 300 $aReproduction of original in the British Library. 330 $aeebo-0018 606 $aTheology, Doctrinal$vEarly works to 1800 607 $aGreat Britain$xChurch history$vEarly works to 1800 615 0$aTheology, Doctrinal 700 $aRosdell$b Christopher$fb. 1553 or 4.$01020316 801 0$bCu-RivES 801 1$bCu-RivES 801 2$bCStRLIN 801 2$bWaOLN 906 $aBOOK 912 $a996390025803316 996 $aA godlie and short discourse$92423106 997 $aUNISA LEADER 05434nam 22005295 450 001 9910971116803321 005 20250730110321.0 010 $a1-4612-1534-X 024 7 $a10.1007/978-1-4612-1534-9 035 $a(CKB)3400000000089589 035 $a(SSID)ssj0000808068 035 $a(PQKBManifestationID)11443631 035 $a(PQKBTitleCode)TC0000808068 035 $a(PQKBWorkID)10775590 035 $a(PQKB)11513692 035 $a(DE-He213)978-1-4612-1534-9 035 $a(MiAaPQ)EBC3076160 035 $a(PPN)237996499 035 $a(EXLCZ)993400000000089589 100 $a20121227d1999 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aProblems and Solutions for Complex Analysis /$fby Rami Shakarchi 205 $a1st ed. 1999. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d1999. 215 $a1 online resource (XI, 246 p. 17 illus.) 300 $a"With 46 illustrations." 311 08$a0-387-98831-9 327 $aI Complex Numbers and Functions -- I.1 Definition -- I.2 Polar Form -- I.3 Complex Valued Functions -- I.4 Limits and Compact Sets -- I.6 The Cauchy-Riemann Equations -- II Power Series -- II.1 Formal Power Series -- II.2 Convergent Power Series -- II.3 Relations Between Formal and Convergent Series -- II.4 Analytic Functions -- II.5 Differentiation of Power Series -- II.6 The Inverse and Open Mapping Theorems -- III Cauchy?s Theorem, First Part -- III.1 Holomorphic Functions on Connected Sets -- III.2 Integrals over Paths -- III.5 The Homotopy Form of Cauchy?s Theorem -- III.6 Existence of Global Primitives Definition of the Logarithm -- III.7 The Local Cauchy Formula -- IV Winding Numbers and Cauchy?s Theorem -- IV.2 The Global Cauchy Theorem -- V Applications of Cauchy?s Integral Formula -- V.1 Uniform Limits of Analytic Functions -- V.2 Laurent Series -- V.3 Isolated Singularities -- VI Calculus of Residues -- VI.1 The Residue Formula -- VI.2 Evaluation of Definite Integrals -- VII Conformal Mappings -- VII.2 Analytic Automorphisms of the Disc -- VII.3 The Upper Half Plane -- VII.4 Other Examples -- VII.5 Fractional Linear Transformations -- VIII Harmonic Functions -- VIII.1 Definition -- VIII.2 Examples -- VIII.3 Basic Properties of Harmonic Functions -- VIII.4 The Poisson Formula -- VIII.5 Construction of Harmonic Functions -- IX Schwarz Reflection -- IX.2 Reflection Across Analytic Arcs -- X The Riemann Mapping Theorema -- X.1 Statement of the Theorem -- X.2 Compact Sets in Function Spaces -- XI Analytic Continuation along Curves -- XI.1 Continuation Along a Curve -- XI.2 The Dilogarithm -- XII Applications of the Maximum Modulus Principle and Jensen?s Formula -- XII.1 Jensen?s Formula -- XII.2 The Picard-Borel Theorem -- XII.6 The Phragmen-Lindelof and Hadamard Theorems -- XIII Entire and MeromorphicFunctions -- XIII.1 Infinite Products -- XIII.2 Weierstrass Products -- XIII.3 Functions of Finite Order -- XIII.4 Meromorphic Functions, Mittag-Leffler Theorem -- XV The Gamma and Zeta Functions -- XV.1 The Differentiation Lemma -- XV.2 The Gamma Function -- XV.3 The Lerch Formula -- XV.4 Zeta Functions -- XVI The Prime Number Theorem -- XVI.1 Basic Analytic Properties of the Zeta Function -- XVI.2 The Main Lemma and its Application. 330 $aThis book contains all the exercises and solutions of Serge Lang's Complex Analy­ sis. Chapters I through VITI of Lang's book contain the material of an introductory course at the undergraduate level and the reader will find exercises in all of the fol­ lowing topics: power series, Cauchy's theorem, Laurent series, singularities and meromorphic functions, the calculus of residues, conformal mappings and har­ monic functions. Chapters IX through XVI, which are suitable for a more advanced course at the graduate level, offer exercises in the following subjects: Schwarz re­ flection, analytic continuation, Jensen's formula, the Phragmen-LindelOf theorem, entire functions, Weierstrass products and meromorphic functions, the Gamma function and the Zeta function. This solutions manual offers a large number of worked out exercises of varying difficulty. I thank Serge Lang for teaching me complex analysis with so much enthusiasm and passion, and for giving me the opportunity to work on this answer book. Without his patience and help, this project would be far from complete. I thank my brother Karim for always being an infinite source of inspiration and wisdom. Finally, I want to thank Mark McKee for his help on some problems and Jennifer Baltzell for the many years of support, friendship and complicity. Rami Shakarchi Princeton, New Jersey 1999 Contents Preface vii I Complex Numbers and Functions 1 1. 1 Definition . . . . . . . . . . 1 1. 2 Polar Form . . . . . . . . . 3 1. 3 Complex Valued Functions . 8 1. 4 Limits and Compact Sets . . 9 1. 6 The Cauchy-Riemann Equations . 606 $aMathematical analysis 606 $aAnalysis 615 0$aMathematical analysis. 615 14$aAnalysis. 676 $a515/.9 700 $aShakarchi$b Rami$4aut$4http://id.loc.gov/vocabulary/relators/aut$061671 701 $aLang$b Serge$f1927-2005.$01160 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910971116803321 996 $aProblems and Solutions for Complex Analysis$94412596 997 $aUNINA